Global Positioning System Reference
In-Depth Information
1100
0100
0011
0001
400
0
0
0
0
100
0
0
P 0
=
0
00 0 0
400 100 0 0
0 100 0 0
00 1 0 04
00 0
00 0
10
4
=
.
E
E
10 4
.
.E
T
P 0
computes to
500 100 0 0
100 100 0 0
0 0 11 10 10 4
00 04 04
T
P 0
=
.
E
.
E
.
E
.
E
The extrapolated covariance, P
()
t
−
=
P
T
+
Q
()
t
computes to
1
0
0
500 100 0 0
100 100 0 0
0 0 11 10 10 4
00 04 0
()
P Q
0
T
+
t
=
0
.
E
.
E
.
E
.
E4
Compute the Kalman Gain Matrix K
The Kalman gain matrix K is computed where
[
]
−
1
() ()
() () ()
()
()
−
−
T
−
T
K
t
=
P HHP HR
t
t
t
t
t
+
t
1
1
1
1
1
1
1
−
T
First compute PH
() ()
t
t
:
1
1
500 100 0 0
100 100 0 0
0 0 11 10 10 4
00 04 04
−
0 548
.
0
0
−
0 548
.
()
()
−
T
PH
t
t
=
1
1
.
E
.
E
1
0
.
E
.
E
0
1
−
2746
.
−
8
.
−
548
.
−
548
.
=
11 10
.
E
10 4
.
E
10 4
.
E
10 4
.
E
−
T
HPH
()( )
t
t
()
t
can then be computed, resulting in a 2
×
2 matrix as shown:
1
1
1
11 10
.
E
10 4
.
E
() ()
()
HPH
t
t
−
T
t
=
1
1
1
10 4
.
E
10 4
.
E
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